Supersymmetric DBI inflation

We discuss a supersymmetric version of DBI (Dirac–Born–Infeld) inflation, which is a typical inflation model in string cosmology. The supersymmetric DBI action together with a superpotential always leads to correction terms associated with the potential into the kinetic term, which drastically change the dynamics of DBI inflation. We find two significant features of supersymmetric DBI inflation. The first one is that ultra-relativistic motion is prohibited to cause inflation, which leads to order of unity sound velocity squared and hence small non-Gaussianities of primordial curvature perturbations. The second one is that the relation between the tensor-to-scalar ratio and the field variation is modified. Then, significant tensor-to-scalar ratio r?0.01$r?0.01$ is possible because the variation of the canonically normalized inflaton can be beyond the reduced Planck scale. These new features are in sharp contrast with those of the standard non-supersymmetric DBI inflation and hence have a lot of interest implications on upcoming observations of cosmic microwave background (CMB) anisotropies by the Planck satellite as well as direct detection experiments of gravitational waves like DECIGO and BBO.     

SUGRA hybrid inflation with shift symmetry

We propose a solution to the η  -problem in supergravity (SUGRA) hybrid inflation using a Nambu–Goldstone-like shift symmetry within a new class of models. The flatness of the tree-level inflaton potential is ensured by shift symmetry invariance of the Kähler potential, while a small symmetry breaking term in the superpotential gives rise to a slope of the potential at loop-level. In the proposed class of inflation models, potentially dangerous couplings between the inflaton and the moduli sector are avoided. We also discuss under which conditions the predicted spectral index can be in agreement with the best-fit-value of the latest WMAP observation ns∼0.96$n_{\mathrm{s}}\sim 0.96$, corresponding to a hilltop-type inflaton potential at loop-level.     

Mimicking trans-Planckian effects in the CMB with conventional physics

We investigate the possibility that fields coupled to the inflaton can influence the primordial spectrum of density perturbations through their coherent motion. For example, the second field in hybrid inflation might be oscillating at the beginning of inflation rather than at the minimum of its potential. Although this effect is washed out if inflation lasts long enough, we note that there can be up to 30e-foldings of inflation prior to horizon crossing of COBE fluctuations while still giving a potentially visible distortion. Such pumping of the inflaton fluctuations by purely conventional physics can resemble trans-Planckian effects which have been widely discussed. The distortions which they make to the CMB could leave a distinctive signature which differs from generic effects like tilting of the spectrum.     

Spectral index and non-Gaussianity in supersymmetric hybrid inflation

We consider a supersymmetric hybrid inflation model with two inflaton fields. The superpotential during inflation is dominated by W=(κS+κ′S′)M ², where S, S′ are inflatons carrying the same U(1) _R charge, κ, κ′ are dimensionless couplings, and M (∼10¹⁵⁻¹⁶ GeV) is a dimensionful parameter associated with a symmetry breaking scale. One light mass eigenstate drives inflation, while the other heavier mass eigenstate is stuck to the origin. The smallness of the lighter inflaton mass for the scalar spectral index n _s ≈0.96, which is the center value of WMAP7, can be controlled by the ratio κ′/κ through the supergravity corrections. We also discuss the possibility of the two field inflation and large non-Gaussianity in this setup.     

Simple single field inflation models and the running of spectral index

The BICEP2 experiment confirms the existence of primordial gravitational wave with the tensor-to-scalar ratio r=0 ruled out at 7σlevel.The consistency of this large value of r with the Planck data requires a large negative running n′sof the scalar spectral index.Herein we propose two types of the single field inflation models with simple potentials to study the possibility of the consistency of the models with the BICEP2 and Planck observations.One type of model suggested herein is realized in the supergravity model building.These models fail to provide the needed n′seven though both can fit the tensor-to-scalar ratio and spectral index.     

Reconstruction of constant slow-roll inflation

Using the relations between the slow-roll parameters and the power spectra for the single field slow-roll inflation, we derive the scalar spectral tilt n_s and the tensor to scalar ratio r for the constant slow-roll inflation, and obtain the constraint on the slow-roll parameter η from the Planck 2015 results. The inflationary potential for the constant slow-roll inflation is then reconstructed in the framework of both general relativity and the scalar-tensor theory of gravity, and compared with the recently reconstructed E model potential. In the strong coupling limit, we show that the η attractor is reached.     

SUSY see-saw and NMSO(10)GUT inflation after BICEP2

Supersymmetric see-saw slow roll inflection point inflation occurs along a MSSM D-flat direction associated with gauge invariant combination of Higgs, slepton and right-handed sneutrino at a scale set by the right-handed neutrino mass \(M_{{\nu }^{c}} \sim 10^{6}\!\,-\,\!10^{13}\) GeV. The tensor to scalar perturbation ratio r～10^?3 can be achieved in this scenario. However, this scenario faced difficulty in being embedded in the realistic new minimal supersymmetric SO(10) grand unified theory (NMSO(10)GUT). The recent discovery of B-mode polarization by BICEP2, changes the prospects of NMSO(10)GUT inflation. Inflection point models become strongly disfavoured, as the trilinear coupling of SUSY see-saw inflation potential gets suppressed relative to the mass parameter favoured by BICEP2. Large values of r≈0.2 can be achieved with super-Planck scale inflaton values and mass scales of inflaton ≥10 ¹³ GeV. In NMSO(10)GUT, this can be made possible with an admixture of heavy Higgs doublet fields, i.e., other than MSSM Higgs field, which are present and have masses of order GUT scale.     

Determination of landau fermi-liquid parameters in si-MOSFET systems

We analyze experimental data in order to evaluate Landau Fermi-liquid parameters. By using row data of recent Shubnikov-de Haas measurements, we derive, as a function of the electron density n _s, results for the compressibility mass of the charged two-dimensional electron gas. The compressibility mass is nearly equal to the transport mass even in the density region where the transport mass has the tendency to diverge. We conclude that Landau Fermi-liquid parameter F ₀^s (n _s) is nearly independent of electron density and close to zero. This result is derived for silicon (100) and silicon (111) surfaces. We also obtain the dependence of F ₁^s (n _s), determining the transport mass, and of F ₀^a (n _s), determining the spin susceptibility.     

Determination of landau fermi-liquid parameters in si-MOSFET systems

We analyze experimental data in order to evaluate Landau Fermi-liquid parameters. By using row data of recent Shubnikov-de Haas measurements, we derive, as a function of the electron density n _s, results for the compressibility mass of the charged two-dimensional electron gas. The compressibility mass is nearly equal to the transport mass even in the density region where the transport mass has the tendency to diverge. We conclude that Landau Fermi-liquid parameter F ₀^s (n _s) is nearly independent of electron density and close to zero. This result is derived for silicon (100) and silicon (111) surfaces. We also obtain the dependence of F ₁^s (n _s), determining the transport mass, and of F ₀^a (n _s), determining the spin susceptibility. The text was submitted by the authors in English.     

Effect of a lattice upon an interacting system of electrons in two dimensions: Breakdown of scaling and decay of persistent currents

The ground state of an electron gas is characterized by the interparticle spacing to the effective Bohr radius ratio r _s = a/a _B ^*. For polarized electrons on a two dimensional square lattice with Coulomb repulsion, we study the threshold value r _s ^* below which the lattice spacing s becomes a relevant scale and r _s ceases to be the scaling parameter. For systems of small ratios s/a _B ^*, s becomes only relevant at small r _s (large densities) where one has a quantum fluid with a deformed Fermi surface. For systems of large s/a _B ^*, s plays also a role at large r _s (small densities) where one has a Wigner solid, the lattice limiting its harmonic vibrations. The thermodynamic limit of physical systems of different a _B ^* is qualitatively discussed, before quantitatively studying the lattice effects occurring at large r _s . Using a few particle system, we compare exact numerical results obtained with a lattice and analytical perturbative expansions obtained in the continuum limit. Three criteria giving similar values for the lattice threshold r _s ^* are proposed. The first one is a delocalization criterion in the Fock basis of lattice site orbitals. The second one uses the persistent current which can depend on the interaction in a lattice, while it becomes independent of the interaction in the continuum limit. The third one takes into account the limit imposed by the lattice to the harmonic vibrations of the electron solid.Received: 20 January 2004, Published online: 18 June 2004PACS: 71.10.-w Theories and models of many-electron systems - 71.10.Fd Lattice fermion models (Hubbard model, etc.) - 73.20.Qt Electron solids     

Observation of magnetic breakdown in double quantum wells

We report on our studies of magnetic breakdown (MB) in coupled GaAs/Al_0.3Ga_0.7As double quantum wells (DQWs) subject to crossed magnetic fields. MB is a failure of semiclassical theory that occurs when a magnetic field causes electrons to tunnel across a gap ink-space from one Fermi surface (FS) branch to another. We study MB in a two-branch FS created by subjecting a DQW to an in-plane magnetic field (B_∥). The principal effect ofB_∥is a distortion in the dispersion curve of the system, yielding a FS consisting of two components, a lens-shaped inner orbit and an hour-glass-shaped outer orbit. The perpendicular field (B_⊥) causes Landau level formation and Shubnikov–de Haas (SdH) oscillations for each branch of the FS. At higher perpendicular fields MB occurs and electrons tunnel throughk-space from one FS orbit to the other. MB is observed by noting which peaks are present in the Fourier power spectrum of the magnetoresistance versus 1/B_⊥at constantB_∥. We observe MB in two DQW samples over a range ofB_∥.     

An Algebraic Approach to the Generalized Symmetrical Double-Well Potential

We have obtained the energy eigenvalues and the corresponding eigenfunctions for the generalized double-well potential in the non-relativistic Schr?dinger equation. We have calculated the creation and annihilation operators directly from the eigenfunction and we have shown these operators satisfy the commutation relation of the SU(2) group. We have expressed the Hamiltonian in terms of the su(2) algebra. Some interesting result including the standard symmetrical double-well potential, reflectionless-type potential and V ₀tanh ²(r/d) potential are also discussed.     

Particle physics models of inflation and curvaton scenarios

We review the particle theory origin of inflation and curvaton mechanisms for generating large scale structures and the observed temperature anisotropy in the cosmic microwave background (CMB) radiation. Since inflaton or curvaton energy density creates all matter, it is important to understand the process of reheating and preheating into the relevant degrees of freedom required for the success of Big Bang Nucleosynthesis. We discuss two distinct classes of models, one where inflaton and curvaton belong to the hidden sector, which are coupled to the Standard Model gauge sector very weakly. There is another class of models of inflaton and curvaton, which are embedded within Minimal Supersymmetric Standard Model (MSSM) gauge group and beyond, and whose origins lie within gauge invariant combinations of supersymmetric quarks and leptons. Their masses and couplings are all well motivated from low energy physics, therefore such models provide us with a unique opportunity that they can be verified/falsified by the CMB data and also by the future collider and non-collider based experiments. We then briefly discuss the stringy origin of inflation, alternative cosmological scenarios, and bouncing universes.     

A built-in scale in the initial spectrum of density perturbations: Evidence from cluster and CMB data

We calculate the temperature anisotropies of the cosmic microwave background (CMB) for several initial power spectra of density perturbations with a built-in scale suggested by recent optical data on the spatial distribution of rich clusters of galaxies. Using cosmological models with different values of the spectral index, baryon fraction, Hubble constant, and cosmological constant, we compare the calculated radiation power spectrum with the CMB temperature anisotropies measured by the Saskatoon experiment. We show that spectra with a spike at 120h ⁻¹ Mpc are in agreement with the Saskatoon data. The combined evidence from cluster and CMB data favors the presence of a peak and a subsequent break in the initial matter power spectrum. Such a feature is similar to the prediction of an inflationary model wherein an inflaton field is evolving through a kink in the potential. Pis’ma Zh. éksp. Teor. Fiz. 66, No. 6, 373–378 (25 September 1997) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Hydrogen incorporation into BN fullerene-like nanostructures: A first-principles study

We performed density functional theory calculations to investigate the possibility of formation of endohedrally H@(BN)_n–fullerene (n: 24, 36, 60) and H@C₆₀ complexes for potential applications in solid-state quantum-computers. Spin-polarized approach within the generalized gradient approximation with the Perdew–Burke–Ernzerhof functional was used for the total energies and structural relaxation calculations. The calculated binding energies show that H atom being incorporated into B₆₀N₆₀ nanocage can form most stable complexes while the B₂₄N₂₄ and C₆₀ nanocages might form unstable complex with positive binding energy. We have also examined the penetration of an H atom into the respective nanocages and the calculated barrier energies indicate that the H atom prefers to penetrate into the B₂₄N₂₄ and B₆₀N₆₀ nanocages with barrier energy of about 0.47 eV (10.84 kcal/mol). Furthermore the binding characteristic is rationalized by analyzing the electronic structures. Our findings reveal that the B₆₀N₆₀ nanocage has fascinating potential application in future solid-state quantum-computers.     

Observational Constraints on the Chaplygin Gas with Inverse Power Law Potential in Braneworld Inflation

We study Chaplygin gas as a candidate for inflation in the context of braneworld inflationary model. We investigate this model in the framework of the Randall–Sundrum type II, considering a original and generalized Chaplygin gas. We use inverse power law potential to examine the behavior of some inflationary spectrum parameters such as the spectral index n_s, the ratio r and the running of the scalar spectral index dn_s/dlnk, our results are in agreement with recent observational data for a particular choice of e-folding number N and parameters space of the model.     

Effects of linking chain length and magnetic field on the kinetics of photoprocesses in covalently bonded porphyrin—viologen dyads

The formation and decay kinetics of chain linked triplet radical pairs derived from photo-induced electron transfer reactions in a series of 21 zinc porphyrin-flexible spacer-viologen (ZnP-Sp _n -Vi²⁺) dyads containing 2–138 atoms (n) in the spacer, have been examined by nanosecond laser flash photolysis techniques in an external magnetic field. In non-viscous polar solvents (acetone and CHCl₃ plus CH₃OH = 1:1 v/v), the effect of the spacer length on the rate constant of forward electron transfer can be described by the equation: k _et = k ⁰ _et(n + 6)^?1.5, with k ⁰ _et = 3 × 10¹⁰ s^?1 and 1.2 × 10¹⁰ s^?1 for electron transfer from the singlet and triplet states of ZnP, respectively. In zero magnetic field, the value of the triplet radical pair recombination rate constant, k _r(0) = 0.7 × 10⁶-8 × 10⁶ s^?1, is significantly smaller than k _et. The dependence of k _r(0) on n has an extremum with the maximum near n = 20. In a strong magnetic field (B = 0.21 T), significant retardation of triplet radical pair recombination is observed. In strong magnetic fields the effect of the chain length on triplet radical pair recombination rates is rather small and k _r(B) may vary in the range 0.3 × 10⁶-1 × 10⁷ s^?1. The phenomena observed are discussed in terms of the interplay of molecular and spin dynamics in the limits of slow and fast encounters, taking into account the exchange-interaction.     

The upper bound on the tensor-to-scalar ratio consistent with quantum gravity

We consider the polynomial inflation with the tensor-to-scalar ratio as large as possible which can be consistent with the quantum gravity(QG) corrections and effective field theory(EFT). To get a minimal field excursion Δ? for enough e-folding number N, the inflaton field traverses an extremely flat part of the scalar potential, which results in the Lyth bound to be violated. We get a CMB signal consistent with Planck data by numerically computing the equation of motion for inflaton ? and using Mukhanov–Sasaki formalism for primordial spectrum. Inflation ends at Hubble slow-roll parameter ■. Interestingly, we find an excellent practical bound on the inflaton excursion in the format ■, where a is a tiny real number and b is at the order 1. To be consistent with QG/EFT and suppress the high-dimensional operators, we show that the concrete condition on inflaton excursion is ■. For n_s= 0.9649,N_e= 55, and ■0.632 MPl, we predict that the tensor-to-scalar ratio is smaller than 0.0012 for such polynomial inflation to be consistent with QG/EFT.     

A bound on the number of bound states in the Schrödinger equation

A boundS _l is given for the number of bound statesn _i in thelth partial wave corresponding to a spherically symmetric potential in non-relativistic quantum mechanics. This bound is given by whereV _a(l, r) is the attractive part of the effective potentialV(r)+l(l+1)/r ². Extensive comparative study ofS _i and the Bargmann inequality is made.